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Question I recently asked a question about the sorites paradox, and I received the following response, which seems to me to have a logical fallacy in it. In other words, the answer below does not seem to "explain" the paradox as much as it "contains" the paradox.... Here is the reply: "Because the paradox itself results from commitments of common sense: (a) some number of grains is clearly too few to make a heap (maybe 15, as you say); (b) some number of grains is clearly enough to make a heap (maybe 15,000); and yet (c) one grain never makes the difference between any two different statuses (heap vs. non-heap, definitely a heap vs. not definitely a heap, etc.). Given commonsense logic, (a)-(c) can't all be true, but which one should we reject? Most philosophers who try to solve the paradox attack (c), but I certainly haven't seen a refutation of (c) that I'd call 'commonsense.'" It seems that point (c) above presupposes that either we have 100% heap or 0% heap; however if we can have a number of grains such that we have 85% heap / 15% not heap at the same time, or 50% heap / 50% not heap at the same time, then there is no paradox. Maybe it is "merely" a question of semantics? We know that "100% either / 100% or" is a convention that does not necessarily fit the "commonsense" world; often times we "know" from "common sense" that something can be part either / part or at the same time. Yet the "logic" that causes the sorites problem to be a paradox is "logic" that insists that only 100% either or 100% or can exist, which seems to violate the "common sense" test. In other words, I do not see a paradox, I see a problem with underlying assumptions and definitions, the lack of clarity in which produces an apparent paradox which is resolved when we examine those underlying assumptions and definitions. Am I missing something? or am I being "too" concrete in a world in which everyone else insists on abstraction?

Accepted:
February 9, 2012

Comments

I supplied the response you found unsatisfying, so thanks for not pretending you were satisfied by it!

You're right that my response did assume that there's only a "yes" or "no" answer to such questions as "Can N grains (for some particular N) make a heap?", "Can N grains definitely make a heap?", and so on. I also claimed that my assumption was an element of common sense.

As I understand it, your counter-proposal is that N grains can be enough to make, for instance, "an 85% heap" (or maybe "85% of a heap") but not "a 100% heap" (or maybe "100% of a heap"). But what's an 85% heap? What's 85% of a heap, except a smaller heap? More plausibly, maybe you're proposing that the statement "N grains can make a heap" is only 85% true rather than 100% true. Proposals of this sort are well-known in the literature on the sorites paradox, usually under the heading of "many-valued logics" (see section 3.4 of the SEP article "Sorites Paradox" that I linked to in my previous reply).

These many-valued approaches face serious problems. For instance:

(1) What's the smallest number N that's enough grains to make a 100% heap (or 100% of a heap, or that makes it 100% true that N grains can make a heap)? I take it there's no non-arbitrary answer, not simply that we can't know or say what the answer is.

(2) The logical systems that go with many-valued approaches produce implausible results: suppose that some N makes the statement "N grains can make a heap" only 50% true; then the clearly false conjunction "N grains can make a heap and N+1 grains can't make a heap" ends up being roughly 50% true, rather than 0% true.

Further problems are mentioned in section 3.4 of the SEP article and discussed thoroughly in Keefe (2000), Chapters 4 and 5, cited in that article. Indeed, I recommend Keefe (2000) as an expert guide to the issues (even though I think she's far too optimistic about the ability of supervaluationism to solve the paradox).

So my advice is to read the SEP articles "Sorites Paradox" and "Vagueness" and then dive into some of the works they cite. There's no substitute for engaging with the writings of those who've thought carefully and systematically for years about this paradox. They've proposed many solutions, including the one you propose yourself. If you discover a many-valued approach that overcomes the objections arrayed against it, please let us know. I'll be very pleasantly surprised!